Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int INF = 1e9 + 7;
const int EPS = 1e-8;
using namespace std;
int main() {
  int n, m;
  cin >> n >> m;
  bool fl = 0;
  if (n > m) {
    fl = 1;
    swap(n, m);
  }
  vector<vector<int> > data(n, vector<int>(m, 0));
  for (int i = 0; i < (fl ? m : n); i++) {
    for (int j = 0; j < (fl ? n : m); j++) {
      if (!fl) {
        cin >> data[i][j];
      } else {
        cin >> data[j][i];
      }
    }
  }
  vector<pair<int, int> > moves;
  for (int i = 0; i < n; i++) {
    int mink = INF;
    for (int j = 0; j < m; j++) {
      mink = min(mink, data[i][j]);
    }
    for (int j = 0; j < m; j++) {
      data[i][j] -= mink;
    }
    for (int k = 0; k < mink; k++) {
      moves.push_back({0, i});
    }
  }
  for (int j = 0; j < m; j++) {
    int cnt = data[0][j];
    for (int i = 0; i < n; i++) {
      if (data[i][j] != cnt) {
        cout << -1;
        return 0;
      }
    }
    for (int i = 0; i < cnt; i++) {
      moves.push_back({1, j});
    }
  }
  cout << moves.size() << endl;
  for (int i = 0; i < moves.size(); i++) {
    if ((!moves[i].first && !fl) || (moves[i].first && fl)) {
      cout << "row ";
    } else {
      cout << "col ";
    }
    cout << moves[i].second + 1 << endl;
  }
}